But he told reporters on Friday that he would not question potential high-court nominees about their views on abortion, saying it was "inappropriate to discuss".
According to a person familiar with the search process, the meetings took place in recent days.
With a narrow 51-49 GOP majority in the Senate, losing any Republican senator could begin to doom a nominee.
"A candidate for this important position who would overturn Roe v. Wade would not be acceptable to me, because that would indicate an activist agenda that I don't want to see a judge have", Collins said Sunday in an interview on ABC's "This Week".
Tobias said federal appeals court judges Raymond Kethledge of MI and Brett Kavanaugh of Maryland are rumored to be the frontrunners to fill the vacant seat.
"One thing that many people say is he does not appear to be part of the Washington swamp, and he is not one of the East Coast elites", said University of Richmond law professor Carl Tobias. There were the four interviews Monday, as well as a conversation with Republican Sen.
Hardiman has served on the 3rd U.S. Circuit Court of Appeals since 2007, after being appointed by President George W. Bush and winning unanimous approval in the Senate.
Like Souter, the Arizona native returned to her home state and served as a visiting appeals court judge, hearing more than 175 cases and serving with all but two of the nation's 13 federal appeals courts.
Golden Retriever Bitten by Rattlesnake While Protecting Owner on Hike in Arizona
Thankfully, Godwin had a guardian angel in Todd. "Of course, I would rather have been bitten by the snake, but he did [instead]. Paula Godwin says she was walking her dog Todd down a trail in Anthem, Arizona when Godwin almost stepped on the reptile.
Supreme Court Justice Anthony Kennedy announced last week that he would retire, opening up a spot on the bench for Trump to nominate his second conservative justice.
The Associated Press has learned that Vice President Mike Pence has met with some of the contenders for the Supreme Court vacancy created by Justice Anthony Kennedy's retirement. Trump also nominated 94 district court judges, with the Senate confirming 20 to date, and 15 judges in other key courts, of which the Senate has confirmed five.
Should all Democrats vote against a Trump nominee, Republicans will only be able to afford to lose one vote. Kennedy often sided with more liberal justices on issues like abortion and gay rights. "And we do have a majority of votes in the Senate that think the Affordable Care Act should not be gutted".
Thapar's supporters say this is a chance for President Trump to make history. The senator's office characterized the call as an interview, but the White House would only say the two spoke. The senator's office confirmed that he spoke with President Trump on Monday - and while the White House made reference to the call, further details weren't disclosed by the administration.
If Trump succeeds in pushing through another pro-life justice, it could mean the end of Roe v. Wade and a rollback of America's abortion regime.
There have also been lobbying efforts around other candidates.
Without Kennedy, the high court will have four justices picked by Democratic presidents and four picked by Republicans, giving Trump the chance to shift the ideological balance toward conservatives for years to come. He drove a taxi to get through law school, and his degrees from Notre Dame and Georgetown give him a non-Ivy League appeal.
"The court could use some perspectives that were forged in different kinds of regions of the country and different kinds of academic backgrounds", said former Michigan Sen.